Active Disturbance Rejection Control for Nonlinear Systems

Preface ix
 
1 Introduction 1
 
1.1 Problem Statement 1
 
1.2 Overview of Engineering Applications 6
 
1.3 Preliminaries 9
 
1.3.1 Canonical Form of ADRC 9
 
1.3.2 Stability for Nonlinear Systems 18
 
1.3.3 Stability of Linear Systems 24
 
1.3.4 Finite-Time Stability of Continuous System 27
 
1.3.5 Stability of Discontinuous Systems 32
 
1.3.6 Proof of Theorem 1.3.11 34
 
1.4 Remarks and Bibliographical Notes 50
 
2 The Tracking Differentiator (TD) 53
 
2.1 Linear Tracking Differentiator 55
 
2.2 Nonlinear Tracking Differentiator 59
 
2.2.1 Second-Order Nonlinear Tracking Differentiator 60
 
2.2.2 High-Order Nonlinear Tracking Differentiator 64
 
2.3 Finite-Time Stable System-Based Tracking Differentiator 69
 
2.3.1 Convergence of Finite-Time Stable System-Based TD 70
 
2.3.2 A Second-Order Finite-Time Stable Tracking Differentiator 75
 
2.4 Illustrative Examples and Applications 77
 
2.4.1 Comparison of Three Differentiators 77
 
2.4.2 Applications to Frequency Online Estimation 81
 
2.4.3 Application to the Boundary Stabilization of Wave Equation 85
 
2.5 Summary and Open Problems 88
 
2.6 Remarks and Bibliographical Notes 89
 
3 Extended State Observer 93
 
3.1 Linear Extended State Observer for SISO Systems 94
 
3.2 Nonlinear Extended State Observer for SISO Systems 100
 
3.2.1 Nonlinear ESO for SISO Systems 101
 
3.2.2 Some Special ESO 109
 
3.3 The ESO for SISO Systems with Time-Varying Gain 119
 
3.4 The ESO for MIMO Systems with Uncertainty 133
 
3.4.1 ESO for Systems with Total Disturbance 133
 
3.4.2 ESO for Systems with External Disturbance Only 141
 
3.4.3 Examples and Numerical Simulations 144
 
3.5 Summary and Open Problems 150
 
3.6 Remarks and Bibliographical Notes 153
 
4 The Active